Effect of adding an Independent Variable in Multiple Linear Regression
Yes, the addition of the independent variable ($X_2$) will have an impact on the beta coefficient of $X_1$.
Maybe, it depends on the relationship between $X_1$ and $Y$, and whether you are using any regularization or not.
If the independent variable $X_2$ is more correlated than $X_1$, then the value of $r^2$ should be higher (but I am not sure on this)